Spectral asymptotics of the Dirichlet Laplacian in a conical layer

DOI10.3934/cpaa.2015.14.1239zbMath1422.35015arXiv1411.6383OpenAlexW3103517717MaRDI QIDQ2339878

Monique Dauge, Thomas Ourmières-Bonafos, Nicolas Raymond

Publication date: 14 April 2015

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.6383

zbMATH Keywords

spectral asymptoticsDirichlet Laplacianconical layers

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (11)

Existence of the discrete spectrum in the Fichera layers and crosses of arbitrary dimension ⋮ Discrete spectrum of interactions concentrated near conical surfaces ⋮ On the bound states of Schrödinger operators with δ-interactions on conical surfaces ⋮ Spectral asymptotics of the Dirichlet Laplacian on a generalized parabolic layer ⋮ Spectral asymptotics for \(\delta\)-interactions on sharp cones ⋮ Existence of discrete eigenvalues for the Dirichlet Laplacian in a two-dimensional twisted strip ⋮ On the Discrete Spectrum of Robin Laplacians in Conical Domains ⋮ Eigenvalue counting function for Robin Laplacians on conical domains ⋮ Discrete spectrum of Schrödinger operators with potentials concentrated near conical surfaces ⋮ Dirichlet spectrum of the Fichera layer ⋮ Spectral transitions for Aharonov-Bohm Laplacians on conical layers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A general effective Hamiltonian method
• Corrections to the classical behavior of the number of bound states of Schrödinger operators
• On the Born-Oppenheimer expansion for polyatomic molecules
• Dirichlet eigenvalues of cones in the small aperture limit
• Plane waveguides with corners in the small angle limit
• Quantum waveguides with corners
• Schrödinger operators withδ-interactions supported on conical surfaces
• Remarks on the spectrum of the Neumann problem with magnetic field in the half-space
• Spectrum of Dirichlet Laplacian in a conical layer
• Multiple wells in the semi-classical limit I
• Bound states in curved quantum waveguides
• Eigenvalues of Schrödinger operators with potential asymptotically homogeneous of degree $-2$
• Topologically nontrivial quantum layers
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
• On the mathematical treatment of the Born-Oppenheimer approximation
• Trapped modes in angular joints of 2D waveguides
• Bound states in curved quantum layers

This page was built for publication: Spectral asymptotics of the Dirichlet Laplacian in a conical layer